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Beliebt Rechnen >

limit as x approaches 0+of 2sqrt(x)ln(x)

Lösung

x \to 0 + lim (2 x ln (x))

Lösung

0

Schritte zur Lösung

x \to 0 + lim (2 x ln (x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 + lim (x ln (x))

Umformung für L'Hopital

= 2 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= 2 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{2 x ^{\frac{3}{2}}}})

Vereinfache

\frac{\frac{1}{x}}{- \frac{1}{2 x ^{\frac{3}{2}}}} : - 2 x^{\frac{1}{2}}

= 2 \cdot x \to 0 + lim (- 2 x^{\frac{1}{2}})

Setze den Wert

x = 0

ein

= 2 (- 2 \cdot 0^{\frac{1}{2}})

Vereinfache

= 0

Graph

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